Existence and stability of forced oscillations in non-linear systems with one degree of freedom

Forced oscillations of one degree of freedom systems are considered. The size of the external periodic force and the non-linearity are not limited while the non-conservative forces are supposed to be small. The qualitative analysis is carried out with the aim of establishing the existence, behavior and stability of harmonic and subharmonic oscillations depending on the position and external forces. Some of the stability criteria obtained justify and generalize the known results established via approximate analytical methods; at the same time, cases are indicated where the application of such methods to stability analysis may result in error.